If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are `A +- sqrt((A+G)(A-G))`.

If A and G are the A.M. and G.M. respectively between any two distinct positive numbers a and b then show that A > G.

If A.M and G.M of two positive numbers are 13 and 12 respectively. Find the numbers.

The A.M. between two positive numbers is 34 and their G.M. is 16. find the numbers.

If one G.M., G and two A.M's p and q be inserted between two given numbers, prove that G^(2)= (2p-q) (2q-p)

If the ratio of A.M and G.M between two numbers is 5:3, then the ratio of two numbers is:

A.M. between two numbers is 10 and their G.M is 8. Find the numbers.

Find two positive numbers m and n whose AM and GM are 34 and 16 respectively.

If the A.M of two numbers is 9 and G.M is 4, then these numbers are roots of the equation:

The ratio of the.A.M. and G.M. of two positive numbers a and b is m : n. Show that a: b = (m + sqrt(m^(2)-n^(2))): (m- sqrt(m^(2)-n^(2)))

If G is the geometric mean between two distinct positive numbers a and b, then show that 1/(G-a)+1/(G-b)=1/G .